Home
Class 12
MATHS
Suppose A=[{:(a,b),(c,d):}] is real mat...

Suppose `A=[{:(a,b),(c,d):}]` is real matrix with nonzero entries, ad-bc=0 , and `A^(2)`=A. Then a+d equals

A

1

B

2

C

3

D

4

Text Solution

Verified by Experts

The correct Answer is:
A
`A^(2)=[{:(a,b),(c,d):}][{:(a,d),(c,d):}] ad =bc implies (a)/(b)=(c)/(d)=k`
`=[{:(a^(2)+bc,ab+bd),(ac+cd,bc+d^(2)):}] a=bk,c=dk`
`a^(2)+bc=a ,b(a+d)=b`
`impliesa+d=1`
Doubtnut Promotions Banner Mobile Dark
|

Topper's Solved these Questions

  • KVPY

    KVPY PREVIOUS YEAR|Exercise PART-2 MATHMATICS|10 Videos

  • KVPY

    KVPY PREVIOUS YEAR|Exercise Part 2 Mathematics|15 Videos

  • KVPY

    KVPY PREVIOUS YEAR|Exercise Part B- Mathematics|10 Videos

  • KVPY 2021

    KVPY PREVIOUS YEAR|Exercise PART II MATHEMATICS|4 Videos

Similar Questions

Explore conceptually related problems

Let A=([a,bc,d]) such that A^(3)=0, then a+d equals

Let A=[[a,b],[c,d]] be a 2xx2 real matrix. If A-alphaI is invertible for every real number alpha , then

Knowledge Check

  • If {:A=[(a,b),(c,d)]:} such that ad - bc ne 0 , then A^(-1) , is

    A
    `1/(ad-bc){:[(a,-b),(-c,a)]:}`
    B
    `1/(ad-bc){:[(a,-b),(-c,a)]:}`
    C
    `{:[(d,b),(-c,a)]:}`
    D
    none of these

  • If A=[(a,b),(c,d)] such that ad-bc!=0 , then A^(-1) is equal to

    A
    `1/(ad-bc)[(d,b),(-c,a)]`
    B
    `[(d,-b),(-c,a)]`
    C
    `1(ad-bc)[(d,-b),(-c,a)]`
    D
    None of these

  • Let A and B be two 2 xx 2 matrix with real entries, If AB=0 and such that tr(A)=tr(B)=0then

    A
    A and B are comutative w.r.t. operations of multiplication
    B
    A and B are not cummulative w.r.t operation of multiplication
    C
    A and B are both null matrices,0
    D
    BA=0

    • Similar Questions

    Explore conceptually related problems

    If A is an orthogonal matrix then A^(-1) equals A^(T) b.A c.A^(2) d.none of these

    If matrix A=[(a,b),(c,d)] , then |A|^(-1) is equal to

    Let a be a matrix of order 2xx2 such that A^(2)=O . A^(2)-(a+d)A+(ad-bc)I is equal to

    If the matrix {:[(a,b),(c,d)]:} is commutative with matrix {:[(1,1),(0,1)]:} , then

    Let A be a 2xx 2 matrix with real entries and det (A)= d ne 0 such that det (A+d(adj ) A)) =0 . Find the valued of det ( A-d(dj (A))

    Home
    Profile